.DVID3B2 STA P+2 \ Set P+2 = AName: DVID3B2 Type: Subroutine Category: Maths (Arithmetic) Summary: Calculate K(3 2 1 0) = (A P+1 P) / (z_sign z_hi z_lo) Deep dive: Shift-and-subtract division
Calculate the following: K(3 2 1 0) = (A P+1 P) / (z_sign z_hi z_lo) The actual division here is done as an 8-bit calculation using LL31, but this routine shifts both the numerator (the top part of the division) and the denominator (the bottom part of the division) around to get the multi-byte result we want. Specifically, it shifts both of them to the left as far as possible, keeping a tally of how many shifts get done in each one - and specifically, the difference in the number of shifts between the top and bottom (as shifting both of them once in the same direction won't change the result). It then divides the two highest bytes with the simple 8-bit routine in LL31, and shifts the result by the difference in the number of shifts, which acts as a scale factor to get the correct result. Returns: K(3 2 1 0) The result of the division X X is preserved
The advanced versions have a check to ensure the DVID3B2 routine doesn't try to divide by zero, a check the other versions lack.
Tap on a block to expand it, and tap it again to revert.
LDA INWK+6 \ Set Q = z_lo STA QLDA INWK+6 \ Set Q = z_lo, making sure Q is at least 1 ORA #1 STA Q
LDA INWK+7 \ Set R = z_hi STA R LDA INWK+8 \ Set S = z_sign STA S .DVID3B \ Given the above assignments, we now want to calculate \ the following to get the result we want: \ \ K(3 2 1 0) = P(2 1 0) / (S R Q) LDA P \ Make sure P(2 1 0) is at least 1 ORA #1 STA P LDA P+2 \ Set T to the sign of P+2 * S (i.e. the sign of the EOR S \ result) and store it in T AND #%10000000 STA T LDY #0 \ Set Y = 0 to store the scale factor LDA P+2 \ Clear the sign bit of P+2, so the division can be done AND #%01111111 \ with positive numbers and we'll set the correct sign \ below, once all the maths is done \ \ This also leaves A = P+2, which we use below .DVL9 \ We now shift (A P+1 P) left until A >= 64, counting \ the number of shifts in Y. This makes the top part of \ the division as large as possible, thus retaining as \ much accuracy as we can. When we come to return the \ final result, we shift the result by the number of \ places in Y, and in the correct direction CMP #64 \ If A >= 64, jump down to DV14 BCS DV14 ASL P \ Shift (A P+1 P) to the left ROL P+1 ROL A INY \ Increment the scale factor in Y BNE DVL9 \ Loop up to DVL9 (this BNE is effectively a JMP, as Y \ will never be zero) .DV14 \ If we get here, A >= 64 and contains the highest byte \ of the numerator, scaled up by the number of left \ shifts in Y STA P+2 \ Store A in P+2, so we now have the scaled value of \ the numerator in P(2 1 0) LDA S \ Set A = |S| AND #%01111111
BMI DV9 \ If bit 7 of A is set, jump down to DV9 to skip the \ left-shifting of the denominator (though this branch \ instruction has no effect as bit 7 of the above AND \ can never be set, which is why this instruction was \ removed from later versions)\BMI DV9 \ This label is commented out in the original source
.DVL6 \ We now shift (S R Q) left until bit 7 of S is set, \ reducing Y by the number of shifts. This makes the \ bottom part of the division as large as possible, thus \ retaining as much accuracy as we can. When we come to \ return the final result, we shift the result by the \ total number of places in Y, and in the correct \ direction, to give us the correct result \ \ We set A to |S| above, so the following actually \ shifts (A R Q) DEY \ Decrement the scale factor in Y ASL Q \ Shift (A R Q) to the left ROL R ROL A BPL DVL6 \ Loop up to DVL6 to do another shift, until bit 7 of A \ is set and we can't shift left any further .DV9 \ We have now shifted both the numerator and denominator \ left as far as they will go, keeping a tally of the \ overall scale factor of the various shifts in Y. We \ can now divide just the two highest bytes to get our \ result STA Q \ Set Q = A, the highest byte of the denominator LDA #254 \ Set R to have bits 1-7 set, so we can pass this to STA R \ LL31 to act as the bit counter in the division LDA P+2 \ Set A to the highest byte of the numerator
JSR LL31 \ Call LL31 to calculate: \ \ R = 256 * A / Q \ = 256 * numerator / denominator.LL31new ASL A \ This contains the code from the LL31 routine, so BCS LL29new \ this section is exactly equivalent to a JSR LL31 CMP Q \ call, but is slightly faster as it's been inlined, BCC P%+4 \ so it calculates: SBC Q \ ROL R \ R = 256 * A / Q BCS LL31new \ = 256 * numerator / denominator JMP LL312new .LL29new SBC Q \ This is also part of the inline LL31 routine SEC ROL R BCS LL31new LDA R .LL312new
\ The result of our division is now in R, so we just \ need to shift it back by the scale factor in Y LDA #0 \ Set K(3 2 1) = 0 to hold the result (we populate K STA K+1 \ next) STA K+2 STA K+3 TYA \ If Y is positive, jump to DV12 BPL DV12 \ If we get here then Y is negative, so we need to shift \ the result R to the left by Y places, and then set the \ correct sign for the result LDA R \ Set A = R .DVL8 ASL A \ Shift (K+3 K+2 K+1 A) left ROL K+1 ROL K+2 ROL K+3 INY \ Increment the scale factor in Y BNE DVL8 \ Loop back to DVL8 until we have shifted left by Y \ places STA K \ Store A in K so the result is now in K(3 2 1 0) LDA K+3 \ Set K+3 to the sign in T, which we set above to the ORA T \ correct sign for the result STA K+3 RTS \ Return from the subroutine .DV13 \ If we get here then Y is zero, so we don't need to \ shift the result R, we just need to set the correct \ sign for the result LDA R \ Store R in K so the result is now in K(3 2 1 0) STA K LDA T \ Set K+3 to the sign in T, which we set above to the STA K+3 \ correct sign for the result RTS \ Return from the subroutine .DV12 BEQ DV13 \ We jumped here having set A to the scale factor in Y, \ so this jumps up to DV13 if Y = 0 \ If we get here then Y is positive and non-zero, so we \ need to shift the result R to the right by Y places \ and then set the correct sign for the result. We also \ know that K(3 2 1) will stay 0, as we are shifting the \ lowest byte to the right, so no set bits will make \ their way into the top three bytes LDA R \ Set A = R .DVL10 LSR A \ Shift A right DEY \ Decrement the scale factor in Y BNE DVL10 \ Loop back to DVL10 until we have shifted right by Y \ places STA K \ Store the shifted A in K so the result is now in \ K(3 2 1 0) LDA T \ Set K+3 to the sign in T, which we set above to the STA K+3 \ correct sign for the result RTS \ Return from the subroutine